Abstract

Most hadron synchrotrons rely on lattice nonlinearities for Landau damping of impedance driven coherent modes of oscillation. However, in a collider, the presence of beam-beam interactions strongly modifies the transverse amplitude detuning and therefore the resulting stability diagram. A numerical tool to evaluate the effect of beam-beam on the stability diagram has been developed and is used to discuss observations during different phases of the operational cycle of the Large Hadron Collider during the 2012 proton run. In particular, we show the evolution of the stability diagram when the strength of long range beam-beam interactions is increased, during the betatron squeeze. Also, we investigate the stability of beams colliding with a small transverse offset and compare to observations of instabilities when bringing the beams into collision and while leveling the luminosity.

Highlights

  • The stability of coherent modes of oscillation driven by the beam coupling impedance is usually ensured by lattice nonlinearities, which cause particles at different betatron amplitude to oscillate at different frequencies, introducing Landau damping of coherent motion [1]

  • The strength of the Landau damping can be described by a stability diagram, which splits the complex plane in two parts determining the stability of a coherent mode characterized by its complex tune shift

  • Analytical derivations of the stability diagram can be found for simple configurations, e.g., considering linear detuning from octupolar magnets, assuming Gaussian or parabolic distribution functions [2,3]

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Summary

Buffat

Brookhaven National Laboratory, Upton, New York 11973, USA (Received 25 June 2014; published 25 November 2014). Most hadron synchrotrons rely on lattice nonlinearities for Landau damping of impedance driven coherent modes of oscillation. In a collider, the presence of beam-beam interactions strongly modifies the transverse amplitude detuning and the resulting stability diagram. A numerical tool to evaluate the effect of beam-beam on the stability diagram has been developed and is used to discuss observations during different phases of the operational cycle of the Large Hadron Collider during the 2012 proton run. We show the evolution of the stability diagram when the strength of long range beam-beam interactions is increased, during the betatron squeeze. We investigate the stability of beams colliding with a small transverse offset and compare to observations of instabilities when bringing the beams into collision and while leveling the luminosity

INTRODUCTION
METHOD
Betatron squeeze
Bringing the beams into collision
Luminosity production
Leveling with a transverse offset
SUMMARY AND OUTLOOK

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